Systems and Methods for Adaptive Write Pre-Compensation

ABSTRACT

Various embodiments of the present invention provide systems and methods for write pre-compensation. For example, various embodiments of the present invention provide methods for modifying magnetic information transfer. The methods include retrieving magnetically represented data from a storage medium, and converting the magnetically represented data to a series of data samples. A preceding pattern and a transition status is identified in the series of data samples, and an equalized channel response is computed based on an estimated NLTS value. An error value is computed that corresponds to a difference between the estimated NLTS value and an actual NLTS value, and a pre-compensation value is computed based at least in part on the error value.

BACKGROUND OF THE INVENTION

The present inventions are related to systems and methods for writinginformation to a magnetic storage medium, and more particularly tosystems and methods for providing pre-compensation for use during astorage medium write.

Writing information to a magnetic storage medium includes generating amagnetic field in close proximity to the storage medium to be written.This may be done using a read/write head assembly as are commonly knownin the art. One problem with such an approach to writing a magneticstorage medium is that the magnetic field generated during the write ofa preceding bit pattern may interfere or otherwise affect a magneticfield generated during a write of a succeeding bit pattern. Inparticular, a magnetic field generated to write a current bit patternmay exhibit a non-linear transition shift (NLTS) caused by magneticinteractions between write-field and already written transitions.Presence of NLTS leads to data-dependent nonlinear distortions in theread back signal, causing degradation in data-recovery performance.Further, where NLTS becomes significant, the media exhibiting the NLTSmay be disqualified, thus resulting in poor yield of the media.

Various systems employ a write pre-compensation scheme that considerspreceding bit patterns in the process of generating a magnetic field towrite a succeeding bit pattern. Such systems search over amulti-dimensional grid to determine the amount of any compensation to beadded to a given write. The criterion used during the search process maybe based on the error rate of the detector or another indicator. Thissearching process is, however, time consuming and becomes almostimpractical for multi-level compensation scenarios where compensationfor several potential patterns must be considered. Moreover, unlike theusual channel optimization tasks, such write compensation demands aseparate write and read for each choice of the compensation. As aresult, a relatively simple compensation scheme (e.g., a single level ora two level compensation scheme) is typically chosen to limit thecomplexity. Such simple compensation schemes are not, however, capableof providing the degree of compensation desired in some applications.

Hence, for at least the aforementioned reasons, there exists a need inthe art for advanced systems and methods for write pre-compensation.

BRIEF SUMMARY OF THE INVENTION

The present inventions are related to systems and methods for writinginformation to a magnetic storage medium, and more particularly tosystems and methods for providing pre-compensation for use during astorage medium write.

Various embodiments of the present invention provide methods formodifying magnetic information transfer. The methods include retrievingmagnetically represented data from a storage medium, and converting themagnetically represented data to a series of data samples. A precedingpattern and a transition status are identified in the series of datasamples, and an equalized channel response is computed based on anestimated NLTS value. An error value is computed that corresponds to adifference between the estimated NLTS value and another calculated NLTSvalue, and a pre-compensation value is computed based at least in parton the error value. In some cases, the estimated NLTS value is apreceding estimated NLTS value. In various instances, thepre-compensation value is operable to compensate for the calculated NLTSvalue. Identifying the preceding pattern may be done in accordance withvarious pre-compensation schemes including, but not limited to, a onelevel pre-compensation scheme, a two level pre-compensation scheme, athree level pre-compensation scheme, or a six level pre-compensationscheme.

In some instances of the aforementioned embodiments, the methods furtherinclude computing a second pre-compensation value using the same seriesof data samples. Thus, in some cases, a single continuous read may beused as the source of multiple pre-compensation values. The series ofdata samples is read in a single read operation from a magnetic storagemedium. In various instances of the aforementioned embodiments, themethods further include eliminating at least one second order term inthe computation of the pre-compensation value, such that the effect ofMR asymmetry is reduced.

In one or more instances of the aforementioned embodiments, the methodsfurther include storing the pre-compensation value in relation to theidentified preceding pattern. A request to write a data set is received,and the pre-compensation value is used in relation to servicing therequest to write the data set. In some cases, using the pre-compensationvalue in relation to servicing the request to write the data setincludes: identifying a write pattern in the data set; and using theidentified write pattern to retrieve the stored pre-compensation value.

In various cases, the magnetically represented data is derived from arandom data pattern previously written to the storage medium. In somecases, the random data pattern is written to the storage medium using asingle continuous write operation. One or more embodiments of thepresent invention further include eliminating at least one second orderterm in the computation of the pre-compensation value to reduce theeffect of MR asymmetry. In some cases, the methods further includeeliminating at least one linear term in the computation of thepre-compensation value to reduce the effect of linear mis-equalization.

Other embodiments of the present invention provide systems fordetermining write pre-compensation values. Such systems include amagnetic storage medium, a read/write head assembly, and apre-compensation value calculation circuit. The pre-compensation valuecalculation circuit includes: an equalizer circuit operable to equalizea data set read from the magnetic storage medium via the read/write headassembly; an equalized channel model circuit that is operable to providean equalized channel response based on at least one estimated NLTSvalue; and an adaptive NLTS estimation circuit that provides at leastthe one estimated NLTS value based in part on the equalized channelresponse and a portion of the equalized data set. In some cases, theequalized channel model circuit is implemented using a processorassociated with a computer readable medium. The computer readable mediumincludes instructions executable by the processor to calculate theequalized channel response based on the at least one estimated NLTSvalue. In various cases, the adaptive NLTS estimation circuit isimplemented using a processor associated with a computer readablemedium. The computer readable medium includes instructions executable bythe processor to calculate the at least one estimated NLTS value.

This summary provides only a general outline of some embodiments of theinvention. Many other objects, features, advantages and otherembodiments of the invention will become more fully apparent from thefollowing detailed description, the appended claims and the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the various embodiments of the presentinvention may be realized by reference to the figures which aredescribed in remaining portions of the specification. In the figures,like reference numerals are used throughout several figures to refer tosimilar components. In some instances, a sub-label consisting of a lowercase letter is associated with a reference numeral to denote one ofmultiple similar components. When reference is made to a referencenumeral without specification to an existing sub-label, it is intendedto refer to all such multiple similar components.

FIG. 1 depicts a storage system with a read channel including anadaptive pre-compensation estimation module in accordance with variousembodiments of the present invention;

FIG. 2 shows one implementation of the adaptive pre-compensationestimation module of FIG. 1 in accordance with one or more embodimentsof the present invention;

FIG. 3 is a flow diagram showing a method in accordance with someembodiments of the present invention for determining and using writepre-compensation values;

FIG. 4 shows another implementation of the adaptive pre-compensationestimation module of FIG. 1 in accordance with other embodiments of thepresent invention;

FIG. 5 depicts an on-the-fly, adaptive pre-compensation estimationsystem in accordance with various embodiments of the present invention;

FIG. 6 is a flow diagram depicting a method for continuous, on-the-flyadaptive pre-compensation in accordance with some embodiments of thepresent invention; and

FIG. 7 is a flow diagram depicting a method for periodic, on-the-flyadaptive pre-compensation in accordance with some embodiments of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

The present inventions are related to systems and methods for writinginformation to a magnetic storage medium, and more particularly tosystems and methods for providing pre-compensation for use during astorage medium write.

Various embodiments of the present invention provide writepre-compensation that adaptively estimates the pre-compensation offsetsusing a parallel approach. In some cases, such pre-compensation offsetsare manifest in the form of a delay, where the delay is designed tocompensate for NLTS such that a write data is written to a desiredlocation on a storage medium. Based on the disclosure provided herein,one of ordinary skill in the art will appreciate other compensationoffsets that may be used in relation to various embodiments of thepresent invention. Unlike existing approaches, such a parallel approachdoes not necessarily involve a serial search and thus uses substantiallyfewer read and write operations to resolve the write pre-compensation.In particular, some embodiments of the present invention utilize asingle random pattern that is read back from the magnetic storage mediumand used to estimate NLTS and pre-compensation values. As used herein,the term “random pattern” is used in its broadest sense to mean anypattern that is not specifically tailored to include a particularpattern of bits. Thus, a random pattern may be derived from apseudo-random pattern generator, or may be bits that have been writtento a storage medium through general use of the storage medium over time.Such a parallel approach substantially reduces the time required todetermine pre-compensation values allowing for an increase inpre-compensation that is performed. Thus, in some embodiments of thepresent invention, only one write and read operation is used todetermine appropriate pre-compensation offsets for a large number ofwrite operations. In other embodiments, multiple writes and reads may beemployed.

In some cases, a read back signal obtained from a magnetic storagemedium is observed at the output of the equalizer. Then, the NLTS delaysare estimated by adaptively minimizing the mean-square error between theequalizer output samples and a model output. The model is constructedfrom the primary equalization target and is parameterized by the NLTSdelays. The adaptive algorithm converges to the NLTS delays. Thepre-compensation offsets are then set as negative of the correspondingNLTS delays. These pre-compensation offsets are then stored to a tablereferenced using the pattern to which the respective pre-compensationoffsets correspond. When a subsequent write operation is performed, theappropriate pre-compensation offset is retrieved from the table andadded to the write process such that it cancels the NLTS.

In some embodiments of the present invention, implementation of theabove described adaptive algorithm is improved. In particular, directapplication of the above described algorithm may not produce a highlyaccurate result due to the affect of mis-equalization on the estimatedNLTS delays and the amount of asymmetry caused by a magneto-resistiveread-head. This is because the nonlinear distortions resulting frommagneto-resistive asymmetry and NLTS have some common terms, leading totheir interaction during adaptive estimation of NLTS. Similarly,presence of NLTS also leads to linear distortion in the read back signalwhich has common terms with mis-equalization. Such embodiments of thepresent invention modify the gradient term by removing most of the termsthat are common between NLTS, mis-equalization and the magneto-resistiveasymmetry.

Turning to FIG. 1, a storage system 100 is depicted including a readchannel 110 with an adaptive pre-compensation estimation module inaccordance with various embodiments of the present invention. Storagesystem 100 may be, for example, a hard disk drive. Read channel 110 mayinclude any adaptive pre-compensation circuitry capable of efficientlydetermining pre-compensation values to be used in one or more writeoperations. As an example, the adaptive pre-compensation circuitry maybe, but is not limited to, that described below in relation to FIG. 2 orFIG. 4. In addition, storage system 100 includes an interface controller120, a hard disk controller 166, a motor controller 168, a spindle motor172, a disk platter 178, and a read/write head 176. Interface controller120 controls addressing and timing of data transfer to/from disk platter178. Disk platter 178 may be any magnetic storage medium known in theart including, but not limited to, a longitudinal magnetic storagemedium or a perpendicular magnetic storage medium. The data on diskplatter 178 consists of groups of magnetic signals that may be detectedby read/write head assembly 176 when the assembly is properly positionedover disk platter 178. In a typical read operation, read/write headassembly 176 is accurately positioned by motor controller 168 over adesired data track on disk platter 178. Motor controller 168 bothpositions read/write head assembly 176 in relation to disk platter 178and drives spindle motor 172 by moving read/write head assembly to theproper data track on disk platter 178 under the direction of hard diskcontroller 166. Spindle motor 172 spins disk platter 178 at a determinedspin rate (RPMs).

Once read/write head assembly 178 is positioned adjacent the proper datatrack, magnetic signals representing data on disk platter 178 are sensedby read/write head assembly 176 as disk platter 178 is rotated byspindle motor 172. The sensed magnetic signals are provided as acontinuous, minute analog signal representative of the magnetic data ondisk platter 178. This minute analog signal is transferred fromread/write head assembly 176 to read channel module 110. In turn, readchannel module 110 decodes and digitizes the received analog signal torecreate the information originally written to disk platter 178. Thisdata is provided as read data 103 to a receiving circuit. A writeoperation is substantially the opposite of the preceding read operationwith write data 101 being provided to read channel module 110. This datais then encoded and written to disk platter 178. Of note, read channelmodule 110 is capable of writing information to disk platter 178 andsubsequently reading the data back. The read back data is used toestimate pre-compensation offsets that may be maintained in a memory.The stored pre-compensation offsets may be retrieved from the memory andused during subsequent writes to compensate for NLTS.

Turning to FIG. 2, an adaptive pre-compensation estimation module 200 isdepicted in accordance with one or more embodiments of the presentinvention. Adaptive pre-compensation estimation module includes apre-compensation determination circuit 201 (shown in dashed lines) and apre-compensated write circuit 202 (shown in dashed lines). In somecases, pre-compensation determination circuit 201 is used during aninitialization process used to generate pre-compensation values, and thepre-compensated write circuit 202 is used during a later write phasethat relies on the earlier generated pre-compensation values.Pre-compensation determination circuit 201 includes an equalizer 210that equalizes a read back signal 205 (e.g., data received from aread/write head assembly). Equalizer 210 may be any circuit known in theart that is capable of performing signal equalization. In one particularembodiment of the present invention, equalizer 210 is a digital finiteimpulse response circuit. Equalizer 210 generates an equalized read backsignal 212, x[n], in accordance with the following equations:

${{x\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}\; {{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{k = {L\; 1}}^{L\; 2}\; {{\hat{\Delta}\lbrack {n - k} \rbrack}{b\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}} + {v\lbrack n\rbrack}}};$and b[n] = a[n] − a[n − 1],

where a[n] is an original write signal 207 provided to an equalizedchannel model circuit 220 via a write buffer 215. For establishingpre-compensation values, a random pattern provided as original writesignal 207 may be preferred over a periodic pattern. Write buffer 215may be any device or circuit capable of receiving the originally writtendata and storing it for later retrieval. Equalized channel model circuit220 provides an equalized channel response 222 based on estimated NLTSvalues 232 in accordance with the following equation:

${d\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}\; {{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{j = 1}^{8}\; {{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}\; {{b_{j}\lbrack {n - k} \rbrack}{{g_{i}\lbrack k\rbrack}.}}}}}}$

Equalized channel response 222 is subtracted from equalized read backsignal 212 using a summation element 235. The output from summationelement 235 is an error, e[n], that is provided to a circuit 230operable to adaptively calculate NLTS estimates 232 and to providepre-compensation values 209. Estimated NLTS values 232 are calculated inaccordance with the following equation:

${{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\; \mu \; {e\lbrack n\rbrack}{\sum\limits_{k = {L\; 1}}^{L\; 2}\; {{b_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}},{{{for}\mspace{14mu} 1} = 1},2,\ldots \mspace{11mu},8.$

Pre-compensation values 209 are calculated to negate the effect ofcorresponding estimated NLTS values 232. In one implementation,pre-compensation values 209 are the negative of corresponding estimatedNLTS values 232. Other approaches for calculating pre-compensationvalues 209 based on NLTS estimates may also be used.

Pre-compensated write circuit 202 includes a memory in which a lookuptable 270 is implemented. Lookup table 270 stores pre-compensationvalues 209 in association with a preceding pattern 211 to which theyrespectively correspond. Said another way, to obtain a pre-compensationvalue associated with a particular pattern, the particular pattern orsome unique variation thereof may be used to address lookup table 270.In particular, lookup table 270 includes a pre-compensation value 272corresponding to a pattern 273, a pre-compensation value 274corresponding to a pattern 275, and a pre-compensation value 276corresponding to a pattern 277. Based on the disclosure provided herein,one of ordinary skill in the art will recognize that practically anyquantity of pre-compensation values corresponding to different patternsmay be stored in lookup table 270. When a particular pattern or a uniquevariation thereof is used to address lookup table 270, the correspondingpre-compensation value is provided as an output 282. A write signal 280is provided to a pre-compensation modification circuit 260 that modifiesthe write signal using output 282. The modification operates to negatethe NLTS identified by pre-compensation determination circuit 201.

It should be noted that while various components of adaptivepre-compensation estimation module 200 are described as “circuits” thatthey may be implemented either as an electronic circuit or as asoftware/firmware circuit. Such software/firmware circuits include aprocessor associated with a memory device that includes instructionsexecutable by the processor to perform the particular functionsdescribed herein. Such processors may be general purpose processors orprocessors specifically tailored to perform a given function dependingupon the particular implementation requirements. In some cases, theprocessor may be designed to perform functions related to more than oneparticular module. In some embodiments of the present invention,adaptive pre-compensation estimation module 200 is implemented entirelyas firmware or software being executed by a processor. In otherembodiments of the present invention, adaptive pre-compensationestimation module 200 is implemented entirely as a dedicated electroniccircuit. In yet other embodiments of the present invention, adaptivepre-compensation estimation module 200 is implemented as a combinationof firmware or software being executed on a processor, and dedicatedelectronic circuitry. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of combinations ofdedicated electronic circuitry and software/firmware that may be used inaccordance with different embodiments of the present invention.

The algorithm implemented by adaptive pre-compensation estimation module200 is more fully developed below. In particular, the output ofequalizer 210 may be expressed as x[n] as defined by the followingequations:

$\begin{matrix}{{x\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}\; {{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{k = {L\; 1}}^{L\; 2}\; {{\hat{\Delta}\lbrack {n - k} \rbrack}{b\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}} + {v\lbrack n\rbrack}}} & ( {1a} ) \\{{b\lbrack n\rbrack} = {{a\lbrack n\rbrack} - {a\lbrack {n - 1} \rbrack}}} & ( {1b} )\end{matrix}$

In these equations, a[n] with a[n]ε {−1,+1} represents original writesignal 207 available from write buffer 215; b[n] with b[n]ε {−2,0,+2}represents a transition sequence corresponding to a[n]; g_(b)[k] denotesthe bit response of the channel up to the output of equalizer 210 fork=0, 1, 2 . . . N_(g); (N_(g)+1) denotes the number of coefficients inthe bit response; g_(i)[k] denotes the corresponding impulse response ofthe equalized channel for k=L1, L+1 . . . L2; {circumflex over (Δ)}[n]denotes the NLTS associated with the transition b[n] and provided asNLTS estimates 232; {circumflex over (Δ)}[n+1] denotes the calculatedNLTS that are provided as pre-compensation values 209; and v[n] denotesthe total noise at the output of equalizer 210.

For simplicity, it is assumed that the mis-equalization component at theoutput of equalizer 210 is included in v[n]. Thus, g_(b)[k] is taken tobe the primary equalization target, where N_(g) is, for example, aninteger value 1 or an integer value 2. Equations 1a and 1b also assume aread/write head assembly used to obtain data from a magnetic storagemedium does not exhibit other significant distortions beyond NLTS.

The following Table 1 shows exemplary pre-compensation values (i.e.,pre-compensation delays expressed as a fraction of a bit period) basedon preceding bit patterns.

TABLE 1 Exemplary Pre-compensation Values Based on Preceding BitPatterns Pattern Index Preceding Bits (Oldest Current BitPre-Compensation k First) {S_(k3), S_(k2), S_(k1)} {Sk0} Value 1 {−1,−1, −1} +1 δ₁ 2 {+1, +1, +1} −1 δ₂ 3 {+1, +1, −1} +1 δ₃ 4 {−1, −1, +1}−1 δ₄ 5 {+1, −1, −1} +1 δ₅ 6 {−1, +1, +1} −1 δ₆ 7 {−1, +1, −1} +1 δ₇ 8{+1, −1, +1} −1 δ₈Using the values from Table 1, NLTS can be expressed as:

$\begin{matrix}{{\hat{\Delta}\lbrack n\rbrack} = {\sum\limits_{k = 1}^{8}{{c_{k}\lbrack n\rbrack}\; \Delta_{k}}}} & (2)\end{matrix}$

where c_(k)[n] are indicator functions assuming values of {0,1} forvalues of k=1, 2, . . . , 8. Said another way, c_(k)[n]=1 denotes anoccurrence of a transition corresponding to the k^(th) row in Table 1 atinstant n. Conversely, c_(k)[n]=0 denotes that a transition thatoccurred at an instant n does not correspond to the k^(th) row inTable 1. Again, using Table 1, the index functions can be definedaccording to the following equation:

$\begin{matrix}{{c_{k}\lbrack n\rbrack} = \frac{\begin{matrix}{( {1 + {S_{k\; 0}{a\lbrack n\rbrack}}} )*( {1 + {S_{k\; 1}{a\lbrack {n - 1} \rbrack}}} )*} \\{( {1 + {S_{k\; 2}{a\lbrack {n - 2} \rbrack}}} )*( {1 + {S_{k\; 3}{a\lbrack {n - 3} \rbrack}}} )}\end{matrix}}{16}} & (3)\end{matrix}$

where {S_(k3), S_(k2), S_(k1), S_(k0)} correspond to the bits of the khpattern of Table 1. Substituting equation (2) into equation (1) yields:

$\begin{matrix}{{x\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{j = 1}^{8}{\Delta_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}} + {v\lbrack n\rbrack}}} & (4)\end{matrix}$

where b_(j)[n]=c_(j)[n]*b[n]. Based on equation (3) and equation (1b),b_(j)[n] can be expressed for j=1, 2, 3, . . . , 8 as equation (5):

b_(j)[n] = {(S_(j 0) − S_(j 1))(1 + S_(j 2)a[n − 2] + S_(j 3)a[n − 3]) + (1 − S_(j 0)S_(j 1))(a[n] − a[n − 1]) + (S_(j 1) − S_(j 0))a[n]a[n − 1] + S_(j 2)(S_(j 0)S_(j 1) − 1)a[n − 1]a[n − 2] + S_(j 2)S_(j 3)(S_(j 0) − S_(j 1))a[n − 2]a[n − 3] + S_(j 2)(1 − S_(j 0)S_(j 1))a[n]a[n − 2] + S_(j 3)(S_(j 0)S_(j 1) − 1)a[n − 1]a[n − 3] + S_(j 3)(1 − S_(j 0)S_(j 1))a[n]a[n − 3] + (S_(j 1) − S_(j 0))(S_(j 2)a[n]a[n − 1]a[n − 2] + S_(j 3)a[n]a[n − 1]a[n − 3] +       S_(j 2)S_(j 3)(S_(j 0)S_(j 1) − 1)(a[n − 1]a[n − 2]a[n − 3] − a[n]a[n − 2]a[n − 3] + S_(j 2)S_(j 3)(S_(j 1) − S_(j 0))a[n]a[n − 1]a[n − 2]a[n − 3]}/16

Using equation (4), the samples at output 222 (i.e., d[n]) can beexpressed as:

$\begin{matrix}{{d\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{j = 1}^{8}{{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}}} & (6)\end{matrix}$

where {circumflex over (Δ)}_(j) are estimated NLTS values 232 for j=1,2, 3, . . . , 8.

NLTS values 232 may be estimated by minimizing the mean-square value ofthe error, e[n]. This is done by adaptively using the knowninstantaneous gradient based least mean-square adaptive algorithm. Theerror signal and its gradients with respect to the NLTS values 232 inthe channel model are given by the following equations:

$\begin{matrix}\begin{matrix}{{e\lbrack n\rbrack} = {{x\lbrack n\rbrack} - {d\lbrack n\rbrack}}} \\{= {{x\lbrack n\rbrack} - {\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} + {\sum\limits_{j = 1}^{8}{{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}}}\end{matrix} & ( {7a} ) \\{\frac{\partial{e\lbrack n\rbrack}}{\partial\Delta_{l}} = {\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}} & ( {7b} )\end{matrix}$

Based on equations (7), the process of the adaptive algorithm forestimating NLTS values 232, {circumflex over (Δ)}_(l)[n+1], is describedby the following equations:

$\begin{matrix}{{{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\mu \; {e\lbrack n\rbrack}{\sum\limits_{{k = {L\; 1}}\;}^{L\; 2}{{b_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}},{{\text{for}\mspace{14mu} 1} = 1},2,\ldots \mspace{14mu},8} & ( {8a} ) \\{{e\lbrack n\rbrack} = {{x\lbrack n\rbrack} - {\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} + {\sum\limits_{j = 1}^{8}{{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}}} & ( {8b} ) \\{{b_{j}\lbrack n\rbrack} = {{c_{j}\lbrack n\rbrack}*{b\lbrack n\rbrack}}} & ( {8c} )\end{matrix}$

In equations (8), μ is the adaptation step size (or adaptation gain),and {circumflex over (Δ)}_(l)[n] denotes the estimate of Δ_(l) at aninstant n (i.e., the l^(th) NLTS value 232).

Computation of the error term, e[n], relies on computation of the bitresponse, g_(b)[k], and the impulse response, g_(i)[k], for theequalized channel. The bit response can be taken as the primaryequalization target of equalizer 210. In some embodiments, this primaryequalization target is two or three taps long (i.e., N_(g) is one ortwo) depending on the desired design. The impulse response is the timebased derivative of the step response. Computing the impulse responsemay be done using a two step process. In the first step, the stepresponse of the channel is determined. For a primary target given byg_(b)[k] for k=0, 1, . . . , N_(g), the following step response isobtained:

$\begin{matrix}{{{g_{s}\lbrack k\rbrack} = {{- 0.5}{\sum\limits_{i = 0}^{Ng}{g_{b}\lbrack i\rbrack}}}},{{{for}\mspace{14mu} k} < 0}} & ( {9a} ) \\{{{g_{s}\lbrack k\rbrack} = {0.5( {{\sum\limits_{i = 0}^{k}{g_{b}\lbrack i\rbrack}} - {\sum\limits_{i = {k + 1}}^{Ng}{g_{b}\lbrack i\rbrack}}} )}},{{{for}\mspace{14mu} 0}<=k<=( {{Ng} - 1} )}} & ( {9b} ) \\{{{g_{s}\lbrack k\rbrack} = {0.5{\sum\limits_{i = 0}^{Ng}{g_{b}\lbrack i\rbrack}}}},{{{for}\mspace{20mu} k}>={Ng}}} & ( {9c} )\end{matrix}$

In this case, k=0 is the instant at which the transition in the inputtakes place. Next, the step response is differentiated to yield theimpulse response. This may be done numerically by taking the differencebetween the step response shifted to the right by ε from that shifted tothe left by ε. The resulting difference is then divided by 2ε. In someembodiments of the present invention, raised-cosine interpolationfilters with excess bandwidth are used to generate the shifted stepresponses, and ε is chosen to be 0.005. Using five tap interpolationfilters, the impulse response is set forth in the following equations:

$\begin{matrix}{{{g_{i}\lbrack k\rbrack} = 0},{{{for}\mspace{14mu} k} < 0}} & ( {10a} ) \\{{{g_{i}\lbrack k\rbrack} = {\sum\limits_{i = 0}^{4}{{f\lbrack i\rbrack}{g_{s}\lbrack {k - i} \rbrack}}}},{{{for}\mspace{14mu} 0}<=k<=( {{Ng} + 3} )}} & ( {10b} ) \\{{{g_{i}\lbrack k\rbrack} = 0},{{{for}\mspace{14mu} k}>={{Ng} + 4}}} & ( {10c} )\end{matrix}$

As an example, where the differentiating filter coefficients are givenby:

[f[0], f[1], . . . , f[4]]=[−0.2593, 0.8584, 0.00, −0.8584, 0.2593],

it is understood that L1=0 and L2=Ng+3. It should be noted that otherfilter lengths may be used in accordance with different embodiments ofthe present invention.

The instantaneous gradients used for adapting NLTS estimates 232 aregiven by:

$\begin{matrix}{{{{Grad}_{l}\lbrack n\rbrack} = {{e\lbrack n\rbrack}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}},{{{for}\mspace{14mu} 1} = 1},2,\ldots \mspace{14mu},8.} & (11)\end{matrix}$

As discussed in relation to equation (1a) above, the error samples,e[n], include residual inter-symbol interference caused bymis-equalization through the noise component, v[n]. Also, based onequation (5) above, the quantities b_(l)[n] contain terms that arelinear in data bits. Mis-equalization can be quite significant,especially where the primary target is short. Since the adaptivealgorithm tries to drive the average gradients to zero, the noiseevident in e[n] and b_(l)[n] imply that NLTS estimates 232 will beaffected by mis-equalization. To alleviate the effect ofmis-equalization, the terms in b_(l)[n] that are linear in data bits areremoved from either b_(l)[n] or from e[n]. In one particular embodimentof the present invention, they are removed from b_(l)[n] by removing

{(S _(j0) −S _(j1))(1+S _(j2) a[n−2]+S _(j3) a[n−3])+(1−S _(j0) S_(j1))(a[n]−a[n−1])}/16

from b_(l)[n] described in equation (5) above.

In addition, where a magneto-resistive read/write head assembly is usedto interact with a magnetic storage medium, the head itself introducesamplitude asymmetry in read back signal 205 (i.e., MR asymmetry). Insome cases, a MR asymmetry compensation circuit in the analog front endof a storage device may be included to reduce the affect of such MRasymmetry. However, even with such analog front end compensation, someresidual amount of MR asymmetry is likely to remain in the signal. ThisMR asymmetry may introduce second-order distortion in read back signal205. Therefore, even in the absence of NLTS, read back signal 205 maycontain second-order products of the data-bits, such as, for example,a[n−k]a[n−1]. Further, the terms b_(l)[n] caused by NLTS also containsecond-order products of the data bits as shown in equation (5). Theseterms are used to distinguish between the rising and fallingtransitions. Since the adaptive algorithm discussed above does notdistinguish the second order terms caused by MR asymmetry, the resultingNLTS estimates 232 will be affected by MR asymmetry. To alleviate thisproblem, the terms that are second-order in data-bits are removed fromb_(l)[n] in equation (8a) above. However, not all of the second orderterms can be removed without eliminating the ability to distinguishbetween rising and falling transitions. As a compromise, someembodiments of the present invention remove some of the second orderterms, but maintain others to assure an ability to distinguishtransitions. Further, for the same reason, fourth order terms are alsoremoved from b_(l)[n]. For example, removal of the above mentioned termsresults in the following implementation (equation (12)) used in relationto one particular embodiment of the present invention:

b_(j)[n] = {[S_(j 3)(S_(j 0) − S_(j 1) − 1)a[n − 3] + S_(j 1)S_(j0))(a[n] − a[n − 1])]S_(j 1) − S_(j 2)a[n − 2] + S_(j 3)(S_(j 0)S_(j 1) − 1)a[n − 1]a[n − 3] − S_(j 3)(S_(j 0) − S_(j 1) − 1)a[n]a[n − 3] + (S_(j 1) − S_(j 0))(S_(j 2)a[n − 2] + S_(j 3)a[n − 3])a[n]a[n − 1] + S_(j 2) − S_(j 3)(S_(j 0)S_(j 1) − 1)(a[n − 1] − a[n])a[n − 2] − a[n − 3]}/16

In such embodiments, b_(l)[n] given by equation (5) is used to calculatethe error terms, e[n], and {circumflex over (b)}_(j)[n] given byequation (12) is used to calculate the gradient.

Turning to FIG. 3, a flow diagram 400 depicts a method in accordancewith some embodiments of the present invention for determining and usingpre-compensation values 209. Flow diagram 400 includes two sections: asection 498 covering functions that would generally be done using apre-compensation determination circuit, and a section 499 coveringfunctions that would generally be done using a pre-compensated writecircuit. Following flow diagram 400, the impulse response (g_(i)[k]) forthe channel is calculated (block 405). In some embodiments of thepresent invention, computing the impulse response is accomplished usinga five tap interpolation filter in accordance with equations (10) whichare restated below for simplicity:

$\begin{matrix}{{{g_{i}\lbrack k\rbrack} = 0},{{{{for}\mspace{14mu} k} < 0};}} \\{{{{g_{i}\lbrack k\rbrack} = {\sum\limits_{i = 0}^{4}{{f\lbrack i\rbrack}{g_{s}\lbrack {k - i} \rbrack}}}},{{{{for}\mspace{14mu} 0}<=k<=( {{Ng} + 3} )};}}{and}} \\{{{g_{i}\lbrack k\rbrack} = 0},{{{{for}\mspace{14mu} k}>={{Ng} + 4}};}}\end{matrix}$

where the bit response (g[k]) is defined by equations (9) which arerestated below for simplicity:

$\begin{matrix}{{{g_{s}\lbrack k\rbrack} = {{- 0.5}{\sum\limits_{i = 0}^{Ng}{g_{b}\lbrack i\rbrack}}}},{{{{for}\mspace{14mu} k} < 0};}} \\{{{{g_{s}\lbrack k\rbrack} = {0.5( {{\sum\limits_{i = 0}^{k}{g_{b}\lbrack i\rbrack}} - {\sum\limits_{i = {k + 1}}^{Ng}{g_{b}\lbrack i\rbrack}}} )}},{{{{for}\mspace{14mu} 0}<=k<=( {{Ng} - 1} )};}}{and}} \\{{{g_{s}\lbrack k\rbrack} = {0.5{\sum\limits_{i = 0}^{Ng}{g_{b}\lbrack i\rbrack}}}},{{{for}\mspace{20mu} k}>={{Ng}.}}}\end{matrix}$

Once the impulse response for the channel is available (block 405), itcan be used to determine pre-compensation values 209 for various bitpatterns received as read back signal 205. In particular, a precedingbit pattern along with a current bit transition status is determined(block 410). In some embodiments of the present invention, determiningthe preceding bit patterns and bit transition status is done inaccordance with equation (1b), equation (3), equation (12), and equation(8c) which are all restated below for simplicity:

${ \mspace{79mu} {{{{b\lbrack n\rbrack} = {{a\lbrack n\rbrack} - {a\lbrack {n - 1} \rbrack}}};}\mspace{79mu} {{{c_{k}\lbrack n\rbrack} = \frac{\begin{matrix}{( {1 + {S_{k\; 0}{a\lbrack n\rbrack}}} )*( {1 + {S_{k\; 1}{a\lbrack {n - 1} \rbrack}}} )*} \\{( {1 + {S_{k\; 2}{a\lbrack {n - 2} \rbrack}}} )*( {1 + {S_{k\; 3}{a\lbrack {n - 3} \rbrack}}} )}\end{matrix}}{16}};}{{b_{j}\lbrack n\rbrack} = {{\{ {\lbrack {{{S_{j\; 3}( {S_{j\; 0} - S_{j\; 1} - 1} )}{a\lbrack {n - 3} \rbrack}} + {S_{j\; 1}S_{j0}}} )( {{a\lbrack n\rbrack} - {a\lbrack {n - 1} \rbrack}} )} \rbrack S_{j\; 1}} - {S_{j\; 2}{a\lbrack {n - 2} \rbrack}} + {{S_{j\; 3}( {{S_{j\; 0}S_{j\; 1}} - 1} )}{a\lbrack {n - 1} \rbrack}{a\lbrack {n - 3} \rbrack}} - {{S_{j\; 3}( {S_{j\; 0} - S_{j\; 1} - 1} )}{a\lbrack n\rbrack}{a\lbrack {n - 3} \rbrack}} + {( {S_{j\; 1} - S_{j\; 0}} )( {{S_{j\; 2}{a\lbrack {n - 2} \rbrack}} + {S_{j\; 3}{a\lbrack {n - 3} \rbrack}}} ){a\lbrack n\rbrack}{a\lbrack {n - 1} \rbrack}} + {S_{j\; 2}{S_{j\; 3}( {{S_{j\; 0}S_{j\; 1}} - 1} )}( {{a\lbrack {n - 1} \rbrack} - {a\lbrack n\rbrack}} ){a\lbrack {n - 2} \rbrack}} - {a\lbrack {n - 3} \rbrack}}}} \}/16};$     and      b_(j)[n] = c_(j)[n] * b[n].

In addition, equalized channel response 222 is computed based onestimated NLTS values 232 (block 415).

${d\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{j = 1}^{8}{{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{{g_{i}\lbrack k\rbrack}.}}}}}}$

In addition, the error term is calculated (block 420) by subtracting theequalized channel response 222 from equalized read back signal 212according to the following equation:

e[n]=x[n]−d[n].

Using the results of the forgoing steps (blocks 410-420), apre-compensation value for the particular preceding bit pattern andtransition status is calculated (block 425). In some embodiments of thepresent invention, calculating the particular pre-compensation value isdone based on an estimated NLTS value that is calculated in accordancewith equation (8a) which is restated below for simplicity.

${{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\mu \; {e\lbrack n\rbrack}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{{\hat{b}}_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}},{{{for}\mspace{14mu} 1} = 1},2,\ldots \mspace{11mu},8.$

The pre-compensation value is calculated to negate the estimated NLTSvalue and in some cases is the negative of the estimated NLTS value.

At this juncture, a pre-compensation value has been calculated for oneparticular input pattern. This value is stored in a memory indexed tothe preceding bit pattern to which it corresponds. It is determinedwhether all of the pre-compensation write values are available bydetermining whether the NLTS values corresponding to each of thepre-compensation values have converged (block 430). It should be notedthat each estimated NLTS value may be calculated a number of times untilthe particular NLTS estimate converges on a particular value. Such anapproach provides for an adaptive determination of the estimated NLTSvalues and corresponding pre-compensation values. Convergence may bedetermined by, for example, subtracting the current estimated NLTS valuefrom a preceding estimated NLTS value for each particular bit patternand determining whether the difference is below an acceptable thresholdvalue. It may be that for each particular bit pattern that thedifference between successive NLTS values must remain below a thresholdvalue for a defined number of occurrences before convergence is deemedto have occurred. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of approaches thatmay be used for testing convergence in accordance with differentembodiments of the present invention. Where one or more estimated NLTSvalues remain to converge (block 430), the bit instance is incremented(block 440) and the processes of blocks 410-440 are repeated for thenext sample of read back signal 205.

Alternatively, where all of the estimated NLTS values for the variouspreceding bit patterns have converged (block 430), the table ofpre-compensation values is prepared for use in relation to writing amagnetic storage medium. It is determined whether a write bit isprepared for writing to the magnetic storage medium (block 450). Where abit is ready for writing (block 450), the preceding bit pattern isdetermined along with the transition status (block 455). Where atransition is indicated, a pre-compensation value corresponding to thedetermined preceding bit pattern is retrieved from the memory (block460), and the write is modified based on the selected pre-compensationvalue retrieved from the memory (block 465). This process of modifyingwrite values based on pre-compensation values retrieved from the memoryis repeated for subsequent write operations. It should be noted thatsome of the equations described in relation to flow diagram 400 areparticular to the generation of eight different pre-compensation values,but that other embodiments of the present invention may be tailored forgenerating a different number of pre-compensation values.

In some cases, it is desirable to simplify the implementation describedabove in relation to FIGS. 2-3 and improve the estimation accuracy.Various modifications may be made to the preceding embodiments thatprovide either or both of improved accuracy and simplification of theimplementation. Table 1 above shows that the first two patternscorresponding to k=1 and k=2 may be used as reference patterns forpatterns (k=3, 5 or 7) and (k=4, 6 or 8), respectively. Without loss ofgenerality, it is possible to set the corresponding reference delays δ₁and δ₂ to zero. Thus, an adaptive algorithm capable of estimating onlysix of the eight NLTS values (i.e., values corresponding to k=3, 4, 5,6, 7, 8) is sufficient. It should be noted that while this discussion isparticular to modifying a eight level pre-compensation to a six-levelpre-compensation, that a similar approach may be applied to modifying adifferent number of pre-compensation levels to a lesser number oflevels.

Further, computation of the equalized channel response, d[n], may bemodified. Since c_(j)[n] are binary valued with c_(j)[n]ε {0,1} and b[n]are ternary values with b[n]ε {−2,0,2}, the quantities b_(j)[n] areternary valued with b_(j)[n]ε {−2,0,2}. Further, the original writesignal a[n] is binary valued with a[n]ε {−1,+1}. Based on these, thecomputation of d[n] can be simplified where an assumption is made that{circumflex over (Δ)}_(j)[n]≈{circumflex over (Δ)}_(j)[n−k], for k=0, 1,2, . . . , Ng+3. Such a simplification is reflected in the followingequations:

$\begin{matrix}{{{d\lbrack n\rbrack} = {{d_{1}\lbrack n\rbrack} - {\sum\limits_{k = 0}^{{Ng} + 3}{{\hat{\Delta}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}},} & ( {13a} ) \\{{{d_{1}\lbrack n\rbrack} = {\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}}},} & ( {13b} ) \\ {{\hat{\Delta}\lbrack n\rbrack} = {\sum\limits_{j = 1}^{8}{{{\hat{\Delta}}_{j}\lbrack n\rbrack}{{b_{j}\lbrack n\rbrack}.}}}} \rbrack & ( {13c} )\end{matrix}$

Of note, the computation of d₁[n] and {circumflex over (Δ)}[n] requireonly additions since a[n]ε {−1,+1} and b_(j)[n]ε {−2,0,2}.

Yet further, from Table 1 above it is noted that S_(j0)=−S_(j1) for j=1,2, . . . , 8. Based on this, the expression for {circumflex over(b)}_(j)[n] can be simplified according to equation (14) as follows:

b̂_(j)[n] = {(−S_(j 3)a[n − 3] + S_(j 1)a[n] − S_(j 1)a[n − 1])S_(j 1)S_(j 2)a[n − 2] − S_(j 3)a[n − 1]a[n − 3] + S_(j 3)a[n]a[n − 3] + S_(j 1)(S_(j 2)a[n − 2] + S_(j 3)a[n − 3])a[n]a[n − 1] − S_(j 2)S_(j 3)((a[n − 1] − a[n])a[n − 2]a[n − 3]}/8

As discussed above, some of the second order terms were removed fromb_(j)[n] to reduce the effects of MR asymmetry. However, because not allof the second order terms were removed, the adaptive estimation stillexhibited some dependency on MR asymmetry. This effect can besubstantial where the MR asymmetry is significant. In a recording systemwhere a significant MR asymmetry remains after the analog front end,near optimal write pre-compensation values are not achievable. Using themodified algorithm, the remaining second order terms from b_(j)[n] canbe removed, thus eliminating the effect of MR asymmetry, even whereresidual MR asymmetry remains high. Removing all of the second orderterms can be accomplished by replacing {circumflex over (b)}_(j)[n] with{hacek over (b)}_(j)[n] which is obtained using the following equations:

{hacek over (b)} _(j) [n]={circumflex over (b)} _(j) [n]+{circumflexover (b)}_(j+1) [n], for j=3, 5, 7; and   (15a)

{hacek over (b)}_(j)[n]=0, for j=4, 6, 8.   (15b)

Using equation (14) and equations (15) together, the simplified {hacekover (b)}_(j)[n] can be expressed as follows:

$\begin{matrix}{{{{{\overset{\Cup}{b}}_{j}\lbrack n\rbrack} = \frac{\begin{Bmatrix}{{{S_{j\; 1}( {{S_{j\; 2}{a\lbrack {n - 2} \rbrack}} + {S_{j\; 3}{a\lbrack {n - 3} \rbrack}}} )}{a\lbrack n\rbrack}{a\lbrack {n - 1} \rbrack}} -} \\{S_{j\; 2}{S_{j\; 3}( {{a\lbrack {n - 1} \rbrack} - {a\lbrack n\rbrack}} )}{a\lbrack {n - 2} \rbrack}{a\lbrack {n - 3} \rbrack}}\end{Bmatrix}}{4}},{{{for}\mspace{14mu} j} = 3},5,{7;}}{and}} & ( {16a} ) \\{{{{\overset{\Cup}{b}}_{j}\lbrack n\rbrack} = 0},{{{for}\mspace{14mu} j} = 4},6,8.} & ( {16b} )\end{matrix}$

Of note, {hacek over (b)}_(j)[n] includes only third order terms.Therefore, by using {hacek over (b)}_(j)[n] in place of {circumflex over(b)}_(j)[n] for updating the NLTS estimates, the estimation of NLTS willbe immune from the amount of MR asymmetry present after the analog frontend. Using equations (17), calculation of the pre-compensation valuesmay be done according to the following equations:

$\begin{matrix}{{{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\mu \; {e\lbrack n\rbrack}{\sum\limits_{k = 0}^{{Ng} + 3}{\begin{pmatrix}{{{\hat{b}}_{l}\lbrack {n - k} \rbrack} +} \\{{\hat{b}}_{l + 1}\lbrack {n - k} \rbrack}\end{pmatrix}{g_{i}\lbrack k\rbrack}}}}}},{{{for}\mspace{14mu} 1} = 3},5,{7;{and}}} & ( {17a} ) \\{{{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{\hat{\Delta}}_{l - 1}\lbrack {n + 1} \rbrack}},{{{for}\mspace{20mu} 1} = 4},6,8,} & ( {17b} )\end{matrix}$

where {circumflex over (b)}_(l)[n] is same as that defined in equation(14) above. Thus, with only minimal changes in the updating equation, athree level pre-compensation strategy is achieved that is immune to anyamount of MR asymmetry present in the channel.

Turning to FIG. 4, an adaptive pre-compensation estimation module 300embodying the aforementioned modifications is depicted in accordancewith other embodiments of the present invention. Adaptivepre-compensation estimation module 300 includes a pre-compensationdetermination circuit 301 (shown in dashed lines) and a pre-compensatedwrite circuit 302 (shown in dashed lines). Pre-compensationdetermination circuit 301 includes an equalizer 340 that equalizes aread back signal 305 (e.g., data received from a read/write headassembly). Equalizer 340 may be any circuit known in the art that iscapable of performing signal equalization. In one particular embodimentof the present invention, equalizer 340 is a digital finite impulseresponse circuit. Equalizer 340 generates an equalized read back signal342, x[n], in accordance with the following equations:

${{x\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{k = {L\; 1}}^{L\; 2}{{\hat{\Delta}\lbrack {n - k} \rbrack}{b\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}} + {v\lbrack n\rbrack}}};$and b[n] = a[n] − a[n − 1],

where a[n] is an original write signal 307 provided via a write buffer345 to a bit response calculation circuit 350, a pattern computationcircuit 315, a transition determination circuit 320, and a computationcircuit 365. Write buffer 345 may be any device or circuit capable ofreceiving the originally written data and storing it for laterretrieval. For establishing pre-compensation values, a random patternprovided as original write signal 307 may be preferred over a periodicpattern.

Bit response circuit 350 receives original write signal 307 from writebuffer 345 and determines a bit response output 352, d₁[n], set forthabove as equation (13b):

${d_{1}\lbrack n\rbrack} = {\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{{g_{b}\lbrack k\rbrack}.}}}$

Bit response output 352 is subtracted from equalized read back signal342 using a summation element 343. An output 357 of summation element343 is an error value denoted by the following equation:

e ₁ [n]=x[n]−d ₁ [n].

Pattern computation circuit 315 receives original write signal 307 andprovides an output 317 indicating which identifiable pattern wasreceived prior to the current bit instance. In this case, there are sixidentifiable patterns—the preceding bit patterns corresponding to k=3,4, 5, 6, 7 and 8 in Table 1 above. It should be noted that fewer or morebit patterns may be identified in accordance with different embodimentsof the present invention. The bit patterns are computed in accordancewith the following equation:

${{c_{j}\lbrack n\rbrack} = \frac{( {1 + {S_{k\; 0}{a\lbrack n\rbrack}}} )*( {1 + {S_{k\; 1}{a\lbrack {n - 1} \rbrack}}} )*( {1 + {S_{k\; 2}{a\lbrack {n - 2} \rbrack}}} )*( {1 + {S_{k\; 3}{a\lbrack {n - 3} \rbrack}}} )}{(16)}},{{{for}\mspace{14mu} j} = 3},4,\ldots \mspace{11mu},8.$

In addition, original write signal 307 is provided to transitiondetermination circuit 320 that yields a transition output 322, b[n],that indicates the occurrence of a transition related to the most recentbit in accordance with the following equation:

b[n]=a[n]−a[n−1].

Output 317 is multiplied by transition output 322 using a multiplier 323to yield a combined output 324, b_(j)[n], which indicates which patternis detected and whether a transition occurred. Based on output 324 andprior NLTS values, {circumflex over (Δ)}_(j)[n], NLTS values 327 can becalculated by an NLTS selector circuit 325 using the following equation:

${\hat{\Delta}\lbrack n\rbrack} = {\sum\limits_{j = 3}^{8}{{{\hat{\Delta}}_{j}\lbrack n\rbrack}{{b_{j}\lbrack n\rbrack}.}}}$

Of note, only six computations (i.e., j=3 to 8) are required to yieldthe entire set of pre-compensation values. NLTS values 327 are providedto an impulse response calculation circuit 330. Impulse responsecalculation circuit 330 provides an impulse response output 332, d₂[n],in accordance with the following equation:

${d_{2}\lbrack n\rbrack} = {\sum\limits_{k = 0}^{{Ng} + 4}{{\hat{\Delta}\lbrack {n - k} \rbrack}{{g_{i}\lbrack k\rbrack}.}}}$

Impulse response output 332 is added to error value 357 using asummation element 359 to yield an overall error output 361, e[n].

Computation circuit 365 receives original write signal 307 and providesan output 367 in accordance with the following equation:

b̂_(l)[n] = S_(l 2)a[n]a[n − 2] − S_(l 1)S_(l 2)S_(l 3)a[n − 3]a[n − 2] − S_(l 2)a[n − 1]a[n − 2] − S_(l 3){a[n − 1]a[n − 3] − a[n]a[n − 3]} + S_(l 1)S_(l 2)a[n]a[n − 1]a[n − 2] − S_(l 2)S_(l 3){a[n − 1] − a[n]}a[n − 2]a[n − 3] + S_(l 1)S_(l 3)a[n]a[n − 1]a[n − 3],      for  1 = 3, 4, …  , 8.

Output 367 is provided to an impulse response circuit 370 that generatesan impulse response output 372, d_(3l)[n], in accordance with thefollowing equation:

${{d_{3\; l}\lbrack n\rbrack} = {\sum\limits_{k = 0}^{{Ng} + 4}{{{\hat{b}}_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}},{{{for}\mspace{14mu} 1} = 3},4,\ldots \mspace{11mu},8.$

Impulse response output 372 is multiplied by overall error output 361using a multiplier 373, and the result thereof is multiplied by μ usinga multiplier 374. A resulting product 376 is added with a prior NLTSvalue 377 available from element 375, and the result is an estimatedNLTS value 378 in accordance with the following equations which are arestatement equation (17) above:

$\begin{matrix}{{{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\; \mu \; {e\lbrack n\rbrack}{\sum\limits_{k = 0}^{{Ng} + 3}{{{\hat{b}}_{l}\lbrack {n - k} \rbrack}{g_{i}\lbrack k\rbrack}}}}}},{{{for}\mspace{14mu} 1} = 3},4,5,6,7,8.} & (17)\end{matrix}$

Pre-compensated write circuit 302 includes a memory in which a lookuptable 380 is implemented. Lookup table 380 stores pre-compensationvalues 379 in association with a prior pattern to which theyrespectively correspond. Pre-compensation values 379 are calculatedbased on the NLTS values 378 to negate the effect of NLTS in the system.In one particular implementation, pre-compensation values 379 are thenegative of respective corresponding NLTS values 378. To obtain apre-compensation value associated with a particular prior pattern 391,the particular pattern or some unique variation thereof may be used toaddress lookup table 380. In particular, lookup table 380 includes apre-compensation value 384 corresponding to a preceding pattern 383, apre-compensation value 386 corresponding to a preceding pattern 385, anda pre-compensation value 388 corresponding to a preceding pattern 387.Based on the disclosure provided herein, one of ordinary skill in theart will recognize that practically any quantity of pre-compensationvalues corresponding to different patterns may be stored in lookup table380. When a particular pattern or a unique variation thereof is used toaddress lookup table 380, the corresponding pre-compensation value isprovided as an output 382. A write signal 390 is provided to apre-compensation modification circuit 394 that modifies the write signalusing output 382. The modification operates to negate the NLTSidentified by pre-compensation determination circuit 301.

It should be noted that while various components of adaptivepre-compensation estimation module 300 are described as “circuits” thatthey may be implemented either as an electronic circuit or as asoftware/firmware circuit. Such software/firmware circuits include aprocessor associated with a memory device that includes instructionsexecutable by the processor to perform the particular functionsdescribed herein. Such processors may be general purpose processors orprocessors specifically tailored to perform a given function dependingupon the particular implementation requirements. In some cases, theprocessor may be designed to perform functions related to more than oneparticular module. In some embodiments of the present invention,adaptive pre-compensation estimation module 300 is implemented entirelyas firmware or software being executed by a processor. In otherembodiments of the present invention, adaptive pre-compensationestimation module 300 is implemented entirely as a dedicated electroniccircuit. In yet other embodiments of the present invention, adaptivepre-compensation estimation module 300 is implemented as a combinationof firmware or software being executed on a processor, and dedicatedelectronic circuitry. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of combinations ofdedicated electronic circuitry and software/firmware that may be used inaccordance with different embodiments of the present invention.

The impulse response may be calculated in accordance with the followingequations (18):

g _(s) [k]=−0.5(g _(b)[0]+g _(b)[1]+g _(b)[2]), for k<=−1;

g _(s)[0]=0.5(g _(b)[0]−g _(b)[1]−g _(b)[2]);

g _(s)[1]=0.5(g _(b)[0]+g _(b)[1]−g _(b)[2]); and

g _(s) [k]=0.5(g _(b)[0]+g _(b)[1]+g _(b)[2]), for k>=2.

g _(i) [k]f[0](g _(s) [k]−g _(s) [k−4])+f[1](g _(s) [k−1]−g _(s) [k−3]),for k=0, 1, 2, 3, 4, 5; and

g _(i) [k]0, for k<=−1 and k>=6.

In one particular case, f[0] is −0.2593 and f[1] is 0.8584.

The adaptation gain, μ, is chosen to control the convergence speed. Aset of values given by 2^(−β) where β ε {24, 25, . . . , 29} has beenfound to be sufficient in some embodiments to cover the desired range.In this case, let M1 be the latency from the equalizer (i.e., equalizer210 or equalizer 340) to the detector output. That is, the data decisioncorresponding to the equalizer output x[n] is â[n+M1]. Then, to computethe model output corresponding to x[n] in adaptive pre-compensationestimation module 300, â[n+M1−m] is needed. Consequently, a[n] shouldcorrespond to â[n+M1]. Thus, the latency between the equalizer outputsamples x[n] and the data bits and transitions that are used in thechannel models is M1.

In some cases, it may be desirable to slow down an update of thepre-compensation values. This may be achieved by updating the NLTSparameters, for example, once in every four, eight or twelve bits (i.e.,Ns). A convenient number may be twelve since in some cases we are usingthree or six NLTS parameters to estimate. A possible procedure for doingthe adaptation once every Ns bits is as follows for the case of sixlevel pre-compensation, however, it should be noted that the proceduremay be modified for performing different levels of pre-compensation. Theprocess begins by initializing the NLTS estimates as {circumflex over(Δ)}_(l)[1]=0, for l=3, 4, . . . 8. From the given target coefficients,g_(b)[k], the impulse response coefficients, g_(i)[k], are calculatedusing equations (18). In addition, G_(l) used for accumulating gradientsis set to zero for l=3, 4, . . . 8.

As a second step, where the index bit n is not a multiple of Ns, e[n]and d[n] are computed using equations discussed above in relation toFIG. 4. Further, the gradients are accumulated in accordance with thefollowing equations:

G_(l)←G_(l)+e[n]*d_(3l)[n]; and

{circumflex over (Δ)}_(l)[n+1]is set equal to {circumflex over(Δ)}_(l)[n] for l=3, 4, . . . , 8. Alternatively, if n is a multiple ofNs, the NLTS estimates are updated in accordance with the followingequation:

{circumflex over (Δ)}_(l) [n+1]={circumflex over (Δ)}_(l) [n]−μ*G _(l),for l=3, 4, . . . , 8.

In addition, G_(l)=0, for l=3, 4, . . . , 8 to allow for accumulatingthe gradients. In one particular embodiment of the present invention, avalue of Ns=12 provides reasonable performance.

Alternatively, it may be the case that only one NLTS values is updatedon each bit period. The procedure for doing the adaptation of one NLTSparameter per bit period is as follows for a six level pre-compensation.First, the NLTS estimates are initialized to zero in accordance with thefollowing equation:

{circumflex over (Δ)}_(l)[1]=0, for l=3, 4, . . . , 8.

From the given target coefficients, g_(b)[k], the impulse responsecoefficients, g_(i)[k], are calculated using equations (18). Inaddition, e[n] is computed using equations discussed above in relationto FIG. 4, and the value of l_(n)=mod(n,6)+3. The estimate of the l_(n)^(th) NLTS parameter is calculated using the equations discussed abovein relation to FIG. 4 where l=l_(n), and {circumflex over(Δ)}_(l)[n+1]={circumflex over (Δ)}_(l)[n] for l≠l_(n). Again, the abovementioned approach can be modified for use in relation to differentlevels of pre-compensation.

Based on the disclosure provided herein, one of ordinary skill in theart will appreciate a number of advantages that may be achieved throughuse of embodiments of the present invention. For example, someembodiments of the present invention provide a non-search based approachfor yielding NLTS estimates and the corresponding pre-compensationvalues. This results in a relatively quick and simple approach fordetermining pre-compensation values. Further, some embodiments of thepresent invention provide an adaptive approach for yielding writepre-compensation values that is relatively easy to implement and isexpandable to cover both single level pre-compensation and multi-levelpre-compensation. Yet further, some embodiments of the present inventionare substantially immune to MR asymmetry evident in the channel. Yetfurther, some embodiments of the present invention can be used as a toolto characterize the amount of non-linear distortion due to NLTS. Basedon the disclosure provided herein, one of ordinary skill in the art willrecognize other advantages and features achievable through use of one ormore embodiments of the present invention.

In some embodiments of the present invention, write pre-compensationvalues are calculated at startup or at some point in the devicefabrication process and the same write pre-compensation values are usedfrom there forward in relation to write operations. Such an approachrelies on relatively static write pre-compensation values, which do notaccount for changes in the read/write head assembly over time. Inparticular embodiments of the present invention, the determination ofwrite pre-compensation values is done periodically by writing apseudo-random pattern to a free location on the storage medium and usingthe written data the pre-compensation values are calculated. Such anapproach allows for addressing changes in the read/write head assemblyover time, but requires rendering the storage medium unusable for aperiod of time. In yet other embodiments of the present invention, writepre-compensation values are determined using user data. In such cases,determination of the write pre-compensation values can be doneon-the-fly in parallel with the processing of user data. Such anapproach allows for the write pre-compensation values to be continuouslyupdated without taking the storage medium out of its normal operationalmode. Continuous updating allows for compensating for changes in theread/write head assembly that occur over time. In some cases, theperiodic updating occurs during defined periods of user operation, andthen is inoperable during other times. For example, continuous updatingmay occur once each twenty-four hours and proceed in parallel withnormal usage of the storage medium. Based on the disclosure providedherein, one of ordinary skill in the art will recognize a variety ofintervals and/or update periods that may be used depending upon variousimplementation and/or operational requirements. In some embodiments ofthe present invention offering continuous update capability, a newpre-compensation value may be calculated on-the-fly and compared with acorresponding, previously stored write pre-compensation value. From thiscomparison it can be determined if the characteristics of the read/writehead assembly have changed such that new write pre-compensation valuesshould be determined. Where new values are needed, such values arecalculated and updated in the various zone tables governing themodification of writes.

Turning to FIG. 5, an on-the-fly, adaptive pre-compensation estimationsystem 500 is shown in accordance with various embodiments of thepresent invention. On-the-fly, adaptive pre-compensation estimationsystem 500 includes a pre-compensation determination circuit 501 (shownin dashed lines) and a pre-compensated write circuit 502 (shown indashed lines). Pre-compensation determination circuit 501 operates inparallel with a standard read data path. The standard read path may beany data path capable of receiving analog data from a storage medium andproviding a digital representation thereof to a requester. In this case,the standard read path includes a pre-amplifier 522 receiving an analogsignal derived from a storage medium, and providing an amplified signalto an analog to digital converter 529. The digital samples from analogto digital converter 529 are provided as a read back signal 505 topre-compensation determination circuit 501, and as an input to a datadetector/decoder 524 circuit that provides read values 526 to arequester. Of note, pre-compensation determination circuit 501 operateson the same data input stream and in parallel to data detector/decoder524.

In some cases, pre-compensation determination circuit 501 is used duringdefined periods to update pre-compensation values 509, or continuouslyto provide a constant update of pre-compensation values 509. The updatedpre-compensation values are later used by pre-compensated write circuit502 to perform data writes to the medium from which analog signal 528 isderived. Pre-compensation determination circuit 501 includes anequalizer 510 that equalizes a read back signal 505 (e.g., data receivedfrom a read/write head assembly), a write buffer 515 that receives andstores an original write signal 507, an equalized channel model 520, anadaptive estimation of NLTS 530 that provides NLTS estimates 532 andpre-compensation values 509. Pre-compensation determination circuit 501operates similar to that discussed above in relation to FIG. 2. Anenable signal 517 is provided to enable operation of pre-compensationdetermination circuit 501. In some cases, enable signal 517 is assertedperiodically such that a continuous update of write pre-compensationvalues occurs only occasionally. In some cases, enable signal 517 isasserted all the time resulting in a constant, continuous update. Inother cases, enable signal 517 is only asserted when it is determinedthat a change may have occurred to an associated read/write headassembly necessitating the calculation of updated write pre-compensationvalues. Determining the need for updated write pre-compensation valuesmay be indicated by an increased error rate detected by datadetector/decoder 524, or a comparison indicating a substantialdifference between a newly calculated write pre-compensation value withone previously stored to a lookup table 570.

Pre-compensated write circuit 502 includes a memory in which a lookuptable 570 is implemented. Lookup table 570 stores pre-compensationvalues 509 in association with a preceding pattern 511 to which theyrespectively correspond. Said another way, to obtain a pre-compensationvalue associated with a particular pattern, the particular pattern orsome unique variation thereof may be used to address lookup table 570.In particular, lookup table 570 includes a pre-compensation value 572corresponding to a pattern 573, a pre-compensation value 574corresponding to a pattern 575, and a pre-compensation value 576corresponding to a pattern 577. When a particular pattern or a uniquevariation thereof is used to address lookup table 570, the correspondingpre-compensation value is provided as an output 582. A write signal 580is provided to a pre-compensation modification circuit 560 that modifiesthe write signal using output 582. The modification operates to negatethe NLTS identified by pre-compensation determination circuit 501.

It should be noted that while various components of adaptivepre-compensation estimation module 500 are described as “circuits” thatthey may be implemented either as an electronic circuit or as asoftware/firmware circuit. Such software/firmware circuits include aprocessor associated with a memory device that includes instructionsexecutable by the processor to perform the particular functionsdescribed herein. Such processors may be general purpose processors orprocessors specifically tailored to perform a given function dependingupon the particular implementation requirements. In some cases, theprocessor may be designed to perform functions related to more than oneparticular module. In some embodiments of the present invention,adaptive pre-compensation estimation module 500 is implemented entirelyas firmware or software being executed by a processor. In otherembodiments of the present invention, adaptive pre-compensationestimation module 500 is implemented entirely as a dedicated electroniccircuit. In yet other embodiments of the present invention, adaptivepre-compensation estimation module 500 is implemented as a combinationof firmware or software being executed on a processor, and dedicatedelectronic circuitry. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of combinations ofdedicated electronic circuitry and software/firmware that may be used inaccordance with different embodiments of the present invention.

Turning to FIG. 6, a flow diagram 600 depicts a method for continuouson-the-fly adaptive pre-compensation in accordance with some embodimentsof the present invention. Following flow diagram 600, it is determinedif data is to be read from a storage medium (block 610). Such adetermination may correspond, for example, to receiving a read requestfrom a requesting device. Where a read request is received (block 610),user data at an address indicated by the read request is retrieved fromthe storage medium (block 670). In an exemplary case, retrieving theuser data includes sensing a magnetic signal on a storage medium andamplifying an analog signal corresponding to the sensed magnetic signal.The analog signal is then converted to a series of digital samples usingan analog to digital converter. The user data is provided to a standarddata path for processing read data (block 675), and the result of thestandard data path is the original data stored to the storage mediumthat is provided as a processed user data output to a requesting device(block 680).

In addition, the retrieved user data (block 670) is provided to apre-compensation estimation circuit. The pre-compensation estimationcircuit operates in parallel to the standard read path and performs apre-compensation value update based on the received user data (block698). Such pre-compensation estimates may be generated adaptively usingthe processes discussed above in relation to FIGS. 2-4. For example, theprocesses of block 698 may be similar to the processes of block 498 ofFIG. 3. The process of reading data, providing the read data to arequesting device, and estimating and updating pre-compensation valuesis performed continuously. When a write to the storage medium is desired(block 650), the write is performed using the most recently updatedwrite pre-compensation value corresponding to the pattern preceding thewrite as was discussed above (block 699).

Turning to FIG. 7, a flow diagram 700 shows a method for periodic,on-the-fly adaptive pre-compensation in accordance with some embodimentsof the present invention. Following flow diagram 700, it is determinedif data is to be read from a storage medium (block 705). Such adetermination may correspond, for example, to receiving a read requestfrom a requesting device. Where a read request is received (block 705),user data at an address indicated by the read request is retrieved fromthe storage medium (block 760). In an exemplary case, retrieving theuser data includes sensing a magnetic signal on a storage medium andamplifying an analog signal corresponding to the sensed magnetic signal.The analog signal is then converted to a series of digital samples usingan analog to digital converter. The user data is provided to a standarddata path for processing read data (block 765), and the result of thestandard data path is the original data stored to the storage mediumthat is provided as a processed user data output to a requesting device(block 770).

In addition, it is determined whether it is time to check whether thepre-compensation values need to be updated (block 710). In some cases,the check period may be associated with a period timer or may beassociated with detection of a certain error rate threshold associatedwith the returned data. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of circumstances thatmay be used in determining whether an update of write pre-compensationvalues is warranted. Where an update check is called for (block 710), aparticular pattern in the received user data is identified (block 720),and a pre-compensation estimate corresponding to the pattern iscalculated (block 725). This calculation may be done using one of theapproaches discussed above in relation to FIGS. 2-4, or using anotherapproach for calculating pre-compensation values. It is determined ifthe pre-compensation value has converged (block 730). Where it has notconverged (block 730), the processes of blocks 720-730 are repeateduntil convergence is obtained. Alternatively, where the pre-compensationvalue for the particular pattern has converged (block 730), a previouslydetermined pre-compensation value corresponding to the same pattern isretrieved from memory (block 735). The newly calculated values and theretrieved value are compared (block 735), and it is determined whetherthere is a substantial difference between the two values (block 740).Where there is not a substantial difference (block 740), the process ofdetermining whether an update is necessary completes.

Alternatively, where there is a substantial difference (block 740), afull update of the pre-compensation values is performed using user dataretrieved from the storage medium (block 750). A substantial differencemay indicate a change in the read/write head assembly warrantingmodified pre-compensation values. The full update of thepre-compensation values includes providing user data to apre-compensation estimation circuit. The pre-compensation estimationcircuit operates in parallel to the standard read path and performs apre-compensation value update based on the received user data (block750). Such pre-compensation estimates may be generated adaptively usingthe processes discussed above in relation to FIGS. 2-4. For example, theprocesses of block 750 may be similar to the processes of block 498 ofFIG. 3. The process of reading data, providing the read data to arequesting device, and estimating and updating pre-compensation valuesis performed periodically upon determination that one or morepre-compensation values have drifted from an earlier calculatedpre-compensation value. When a write to the storage medium is desired(block 790), the write is performed using the most recently updatedwrite pre-compensation value corresponding to the pattern preceding thewrite as was discussed above (block 799).

It should be noted that the methods discussed in relation to FIG. 6 andFIG. 7 may be adapted for use in relation to adaptive pre-compensationestimation module 300 of FIG. 4 or other write pre-compensationcalculation systems. The modification involves providing the read backdata from user data either continuously or periodically as discussed inrelation to the foregoing figures.

In conclusion, the invention provides novel systems, devices, methodsand arrangements for performing write pre-compensation. While detaileddescriptions of one or more embodiments of the invention have been givenabove, various alternatives, modifications, and equivalents will beapparent to those skilled in the art without varying from the spirit ofthe invention. Therefore, the above description should not be taken aslimiting the scope of the invention, which is defined by the appendedclaims.

1. A method for modifying magnetic information transfer, the methodcomprising: retrieving magnetically represented data from a storagemedium; converting the magnetically represented data to a series of datasamples; identifying a preceding pattern and a transition status in theseries of data samples; computing an equalized channel response based onan estimated NLTS value; computing an error value, wherein the errorvalue corresponds to a difference between the estimated NLTS value and apreviously estimated NLTS value; and computing a pre-compensation valuebased at least in part on the error value.
 2. The method of claim 1,wherein the pre-compensation value is operable to compensate for theestimated NLTS value.
 3. The method of claim 1, wherein the estimatedNLTS value is a first estimated NLTS value; wherein the previouslyestimated NLTS value is a first previously estimated NLTS value; whereinthe pre-compensation value is a first pre-compensation value; whereinthe preceding pattern is a first preceding pattern; wherein theequalized channel response is a first equalized channel response;wherein the error value is a first error value; and wherein the methodfurther comprises: identifying a second preceding pattern in the seriesof data samples; computing a second equalized channel response based ona second estimated NLTS value; computing a second error value, whereinthe second error value corresponds to a difference between the secondestimated NLTS value and a second previously estimated NLTS value; andcomputing a second pre-compensation value based at least in part on thesecond error value.
 4. The method of claim 3, wherein the first errorvalue and the second error value are computed using the samemagnetically represented data derived from a single read operation. 5.The method of claim 4, wherein the series of data samples are obtainedduring a single, continuous read of the storage medium.
 6. The method ofclaim 1, wherein the magnetically represented data is derived from arandom data pattern previously written to the storage medium.
 7. Themethod of claim 6, wherein the random data pattern is written to thestorage medium using a single continuous write operation.
 8. The methodof claim 1, wherein the pre-compensation value includes at least onesecond order terms, and wherein the method further comprises:eliminating at least one of the at least one second order terms in thecomputation of the pre-compensation value, wherein the effect of MRasymmetry is reduced.
 9. The method of claim 1, the method furthercomprising: storing the pre-compensation value in relation to theidentified preceding pattern.
 10. The method of claim 9, the methodfurther comprising: receiving a request to write a data set; and usingthe pre-compensation value in relation to servicing the request to writethe data set.
 11. The method of claim 10, wherein using thepre-compensation value in relation to servicing the request to write thedata set includes: identifying a write pattern in the data set; andusing the identified write pattern to retrieve the storedpre-compensation value.
 12. The method of claim 1, wherein the methodfurther comprises: computing an impulse response, wherein the impulseresponse is used in relation to computing the error value.
 13. Themethod of claim 1, wherein the storage medium is selected from a groupconsisting of: a longitudinal magnetic storage medium and aperpendicular magnetic storage medium.
 14. The method of claim 1,wherein the pre-compensation value includes at least one linear term,and wherein the method further comprises: eliminating at least one ofthe at least one linear terms in the computation of the pre-compensationvalue, wherein the effect of linear mis-equalization is reduced.
 15. Themethod of claim 1, wherein the preceding pattern is identified inaccordance with a pre-compensation scheme selected from a groupconsisting of: a one level pre-compensation scheme, a two levelpre-compensation scheme, a three level pre-compensation scheme, and asix level pre-compensation scheme.
 16. A system for determining writepre-compensation values, the system comprising: a magnetic storagemedium; a read/write head assembly; a pre-compensation value calculationcircuit, wherein the pre-compensation value calculation circuitincludes: an equalizer circuit operable to equalize a data set read fromthe magnetic storage medium via the read/write head assembly; anequalized channel model circuit, wherein the equalized channel model isoperable to provide an equalized channel response based on at least oneestimated NLTS value; and an adaptive NLTS estimation circuit, whereinthe adaptive NLTS estimation circuit provides at least the one estimatedNLTS value based in part on the equalized channel response and a portionof the equalized data set.
 17. The system of claim 16, wherein theequalized channel model circuit is implemented using a processorassociated with a computer readable medium, and wherein the computerreadable medium includes instructions executable by the processor tocalculate the equalized channel response based on the at least oneestimated NLTS value.
 18. The system of claim 17, wherein the equalizedchannel response is calculated based on the following equation${d\lbrack n\rbrack} = {{\sum\limits_{k = 0}^{Ng}{{a\lbrack {n - k} \rbrack}{g_{b}\lbrack k\rbrack}}} - {\sum\limits_{j = 1}^{8}{{\hat{\Delta}}_{j}{\sum\limits_{k = {L\; 1}}^{L\; 2}{{b_{j}\lbrack {n - k} \rbrack}{{g_{i}\lbrack k\rbrack}.}}}}}}$19. The system of claim 16, wherein the adaptive NLTS estimation circuitis implemented using a processor associated with a computer readablemedium, and wherein the computer readable medium includes instructionsexecutable by the processor to calculate the at least one estimated NLTSvalue.
 20. The system of claim 19, wherein the at least one estimatedNLTS value is calculated based on the following equation:${{{\hat{\Delta}}_{l}\lbrack {n + 1} \rbrack} = {{{\hat{\Delta}}_{l}\lbrack n\rbrack} - {2\; \mu \; {e\lbrack n\rbrack}{\sum\limits_{k = 0}^{{Ng} + 3}{( {{{\hat{b}}_{l}\lbrack {n - k} \rbrack} + {{\hat{b}}_{l + 1}\lbrack {n - k} \rbrack}} ){g_{i}\lbrack k\rbrack}}}}}},$wherein 1 is a defined integer value indexing the at least one estimatedNLTS value.